Question

In the digital circuit shown in the figure, for the given inputs the P and Q values are:

• A. \( P = 1, Q = 1 \)
• B. \( P = 0, Q = 0 \)
• C. \( P = 0, Q = 1 \)
• D. \( P = 1, Q = 0 \)

Hint:

When analyzing logic circuits, work step by step through each gate (AND, OR, NOT) to determine the final outputs.

Answer 1

The Correct Option is B

We are given a digital logic circuit where both inputs are logic 1 (HIGH). We need to determine the outputs \( P \) and \( Q \).

Concept Used:

Each logic gate performs a standard Boolean operation:

• AND gate: Output = 1 only if all inputs are 1.
• NAND gate: Output = NOT(AND) = 0 only if all inputs are 1.
• OR gate: Output = 1 if at least one input is 1.
• NOT gate (inverter): Output = complement of the input.
• NOR gate: Output = NOT(OR).

Step-by-Step Analysis:

Step 1: Identify inputs.

Both upper and lower inputs are given as logic 1 (HIGH).

Step 2: Top-left gate:

It is a NAND gate (AND gate with a bubble at output). Inputs = 1 and 1 → AND output = 1 → NAND output = NOT(1) = 0. \[ \text{Output of NAND gate} = 0 \]

Step 3: The output of this NAND gate (0) goes to two places:

- One input of the lower-left OR gate. - One input of the rightmost AND gate (for P).

Step 4: Bottom-left part:

The OR gate receives two inputs: - One is directly 1 (the lower input line). - The other is 0 (from the NAND gate). So OR output = 1.

Step 5: The OR gate output passes through a NOT gate:

NOT(1) = 0.

Step 6: This 0 goes into the NOR gate (the second circle with OR shape + bubble at output) along with the direct upper input (1).

NOR gate inputs: 1 and 0 → OR = 1 → NOR output = NOT(1) = 0. \[ Q = 0 \]

Step 7: Now find P:

The rightmost top AND gate receives: - One input = output of the first NAND = 0. - Another input = top input = 1. AND(1, 0) = 0. \[ P = 0 \]

Final Computation & Result

\[ P = 0,\quad Q = 0. \]

Correct Option: (2) \( P = 0, Q = 0 \)

Answer 2

For the given digital circuit, follow the logic gates step by step. 
Using the inputs \( P = 0 \) and \( Q = 1 \), we compute the outputs as follows: 
- The AND gate gives \( 0 \) 
- The NOT gate inverts the inputs appropriately. 
Hence, the correct output for the given circuit is: \[ P = 0, Q = 0 \]